Simulating and Identifying Platoon Players

Andre Ethier has one of the most notable splits against right-handed pitching (via Ron Gallegos).

Platoons, they are great when they work out. The thought of two seemingly overlooked players coming out of nowhere and teaming up for some serious production piques my interest. The thought of a platoon performing at an all-star level for a fraction of the price is even more exciting.

The Latin root of platoon means “small ball,” perhaps a sign that platoons are by definition a form of small ball strategy. It would make sense given that most small market teams, who consign to the small ball strategy, utilize platoons in order to gain an advantage over teams with deeper pockets. Whether platooning is a “small ball” strategy is debatable, as you could make a good case that every team should use platoons to their advantage regardless of the elasticity of their budget. I would argue that the necessity to platoon has as much to do with positional scarcity as anything else.

Look no further than the middle infield and catcher situation in baseball.

It is no secret that certain positions are lacking offensive talent more than others. Positional scarcity does come with some selection biases, of course. Most MLB teams will take a weak-hitting shortstop over one who can smash the cover off the ball but can’t field a lick (Jose Iglesias vs. Jhonny Peralta comes to mind). And in any case where the weak hitting middle-infielder wins over the slugger, the slugger is often moved to a corner position on the infield or in the outfield. This is why we see so many platoons on the corners and less up the middle—there is a small pool of player’s who can play the field up the middle at catcher, second base, shortstop, and center field. With a small pool it is harder to pair up two guys who complement each other and play the defense required at that position.

So if an MLB team resigns itself to the fact that they would rather have a Brendan Ryan playing short, they can compensate at positions with a larger (and more variable) skill pool of players. That means teams should take any advantage to platoon at a position where the variation in fielding performance is minimal but where there is plenty of variation in a batter’s value. If that is the case, this means one can easily find two players to hit either side of the platoon and not lose too much defensively, relative to other positions, such as catcher and shortstop. I don’t have the data, but if I would guess that designated hitter, first-base, and outfield are likely the positions with the most platoons historically.

Position pools aside, there is plenty of variation in year to year platoon performance. So a guy who is part of a successful platoon one year can find himself in the gutter the next. This luck factor makes playing the platoon game a little bit like the stock market. First you have to find the platoon players, then you have to flip them when their value is the highest before they regress dramatically. This is because it takes an enormous amount of time for platoon splits to become reliable — it takes nearly 1,000 plate appearances — and 2,000 PA* against lefties and righties respectively — for wOBA to stabilize (where past performance becomes more indicative of future performance than regression to the mean). Now, many platoon players don’t get the chance to accumulate that many plate appearances for us to isolate their true platoon value. For that reason, so many “platooners” are the ones who establish themselves quickly—or are veterans with diminishing skill a strong split to a certain side.

So, isolating platoon players is no easy task. Today, I will show a way to isolate for those who would benefit from platooning.

*Note: In “The Book” there is a great chapter on platoon split regression. Some of that methodology is implemented here, but we will go about it differently in estimating random variance in platoon wOBA.

Methodology

For those into the details, please follow along: To isolate players who would be best suited under the label “platoon player,” I took a three-year weighted average of the player’s platoon splits by simple counting statistics that comprise wOBA (plate appearances, singles, doubles, triples, homers, walks, intentional walks, hit by pitches, sacrifice flies). Then using a resampling method called Bootstrapping, I resampled those components for 1,000 player seasons—projecting the uncertainty in their numbers versus lefties and righties. By taking the projected distribution of each of those components for each “simulated season” I calculated the two distributions of wOBA for each player, one projected wOBA against solely lefties and the other against only righties. Basically, we are simulating what 1,000 player seasons would look like for each player if he faced only one handedness. Given those two distributions, we can pull the mean wOBA and the standard deviation of those projections. Using the uncertainty of the wOBA versus left/right we will regress it towards the mean of all similar players and the population variance. The regression formula, as suggested by Beyond the Boxscore’s statistical guru Stephen Loftus, is as follows:

μwOBA +1/ (1+swOBA / σwOBA) * (wOBA-μwOBA)

Where μwOBA is mean wOBA for versus left/right, swOBA is the standard deviation of the wOBA from the bootstrap versus left/right, σwOBA is the population standard deviation versus left/right and wOBA is mean projection from the bootstrap versus left/right.

Now, Bootstrapping isn’t usually used to simulate per se, but it is meant to be used exactly for our purposes—calculate standard deviation of something very obscure like wOBA. Admittedly, there are probably easier ways to estimate a player’s platoon performance (like those in The Book), but this method will provide us with more in-depth analysis by introducing the measured uncertainty of each player’s wOBA rather than using a generalized approximation.

Lastly, it is important to know that this is in no way a prediction of actual platoon split performance for next year. This is a theoretical simulation of how a player would perform if he faced a certain handedness in every single one of his PAs. In other words, this is not meant to compete with the projection giants of Steamer, ZiPS, Marcel, Oliver, etc. So don’t try to use these numbers to predict next year’s overall performance. Rather this is a way to regress what we know about split performance given recent performance using the uncertainty in each player’s split performance, based on sample size and the components in wOBA. In the process, we’re looking to identify the league’s top prospective platoon players at each position.

Our sample is all players who played in two out of the last three seasons, with at least 150 PA against righties and 100 versus lefties.

Results

We will go through each position and show which players are the “best options” to be platooned at that position; we will present their projected wOBA versus right and left—representing their simulated and regressed performance against both hands. We converted each wOBA into a z-score and picked those from each position who had the largest difference in z-scores. So these are the players who would most benefit from the platoon. To go further, I created “Platoon Score,” which is the z-score of the side of interest multiplied by the difference in the two z-scores. This way we are isolating players with high wOBA against that handedness we are interested in but also taking into account those who are deficient against the other hand. This way we don’t get a lists full of Miguel Cabrera‘s and Mike Trout‘s—as you may know, good hitters trump large platoon splits any day and the point of this exercise is not to tell us who are baseball’s best hitters. Thus, to classify any platoon player they must be above average against one hand and around, or below average, against the other. DH’s were placed in separate positions, as DH platoons could include anyone with minimum defensive value.

Catcher

Of the three above, Jaso is the only one that finds himself currently platooned. Avila, who has been horrendous against lefties in recent seasons and a below average defender, is a fine candidate to be opposite of another catcher in a platoon. A personal favorite of mine, Jason Castro, had a fine year against lefties last year (0.328) but has a 0.227 career wOBA against southpaws.

The other member of the A’s top notch catching platoon, Norris, ranks top amongst the left platoon candidates for backstop. Navarro is a heavy favorite of the simulation after his huge year versus lefties last year at a wOBA of 0.478. I would lean more conservative on the Navaro projection; however, he is definitely one of the top catchers when it comes to hitting lefties. Perez is a good example of a guy whose value on defense makes up for his large platoon split. That being said, Norris makes the perfect platoon candidate given his success in that role with a pretty large sample size.

First Base

Adam Lind is a favorite righty smasher of the sample, with A’s slugger Brandon Moss ranking with the highest wOBA against righties for first basemen we called platoon players. Give me a minute to address the Ryan Howard selection. I didn’t control for salary for a reason—to make a distinction between perceived talent (based on how much a team paid a player) and actual observable performance over the last three years. For that reason, Howard could be best utilized in the platoon role or, if health is there and money is eaten, could make for a interesting trade candidate for a team thinking of a platoon role at 1B.

The pool of lefty smashers at first base is very small relative to those available at first with a tendency to hit righties better. Gaby Sanchez is the only one of the five to really stand out with his proven track record to give lefties trouble. Guzman, who figures to be semi-platooned this season with the Astros, is one of the stronger first basemen against lefties in the platoon sample.

Second Base

Second basemen with a righty favored platoon split are hard to come by. Hence, we see three regulars come out on top of our simulations for this group. The opposite is true for the pool of second basemen with lefty platoon splits.

Here the pool is much stronger with 17 candidates as opposed to four for the group above. However, the candidates at this position are more clustered around a mean of 0.342 wOBA versus lefties—meaning that these three candidates are more valuable given the actual spread of talent in the positional pool. We will get to adjusting for positional talent later, but keep note. Jeff Baker and Kevin Frandsen have been quite good versus lefties for many seasons, while Brian Doizer, despite a heavy regression based on small sample size, has put up impressive numbers in a short period of time.

Third Base

Switch hitter Betemit comes out on top given his atrocious wOBA against lefties in recent history, but Chavez—who has been a part of his fair share of platoons—has the largest simulated wOBA versus right of the three. Pedro Alvarez makes up for his platoon split by his average-ish defensive ability and his moonshots. The matter of the fact is, there aren’t a lot of options at this position to make a platoon at this position worthwhile.

Valencia and Plouffe provide some pop at the corner, with minimum defensive abilities. Prado’s versatility makes him platoon prohibitive, but he does exhibit somewhat of a lefty bias. Cody Ransom (0.346 wOBAleft) and Ryan Roberts (0.341 wOBAleft) come in close behind, as members of previous attempted platoons.

Shortstop

Perpetual free-agent Stephen Drew ranks highly as a platoon-able shortstop, with Didi Gregorius serving as the only other platoon-able player at this position. Jimmy Rollins coming in third with a 0.2 Platoonscore tells you a lot about the platoon depth at this position. This probably has to do with teams valuing defensive over offensive ability at shortstop, meaning there are more light hitters at the position than any other.

Here I would take Jordy Mercer’s projection conservatively despite the heavy regression—due to his small sample versus lefties. That being said lefty platoon splits are more variable, so his small sample is not regressed as much as it would be if he had a righty biased platoon split. Jeter over the last three seasons has been more or less a platoon shortstop, where he is still elite versus southpaws. Cabrera, another switch hitter, has always had a large split but has remained a regular due to his incredible speed.

You will have a hard time convincing a fan-base that platooning Shin-Soo Choo or Jacoby Ellsbury is a good move. I would have to add it’s scary when high OBP/speed guy ages with a large platoon split. It will be interesting to keep our eye on Choo and Ellsbury as they lose value with their legs and power relative to their position. Parra, Smith, DeJesus have all been platooned in the past—and successfully. You can make the case that Either should have been platooned a long time ago, and the numbers would agree with you. The pool of outfielders who would be categorized as “right platooners” is easily the largest and most variable, in terms of platoon score. This means it is easiest to find hitters in the outfield who can hit righties well above average so that the risks of the platoon are outweighed by the reward. Try finding more options at a position like third base or catcher. In terms of a platoon, DH’ing any two outfielders with minimum defensive skills would also be an option.

For outfield versus lefties we have less high priced options—thus they are more easily attainable. Cody Ross, Chris Denorfia, and Jonny Gomes are all players who jump out at me as guys I anticipated seeing. The mean wOBA here is less than those in the group above (0.342 vs. 0.333) but the pool remains just as large (36 versus 33). Given this information, it is easy to see why so many of baseball’s platoons are in the outfield as opposed to the infield. In the outfield, there is less defensive skill required than a shortstop or catcher and a large pool of applicants who have a high mean wOBA compared to other positions.

Positional Analysis

Given all the information I presented above the next logical step is to run some positional analysis. How practical is it to platoon each of these player’s given the skill pool at each position? Below is a table of some summary statistics for those 173 platoon players (out of 431) that we isolated for.

NOTE: Here everything is an average, N is number (pool), and STDEV is the standard deviation of the platoon score for that position.

Platoon Player Summary Statistics

Positional Left

Positional Right

Pos

N

wOBA left

wOBA right

Diff

Platoon Score

STDEV

Pos

N

wOBA right

wOBA left

Diff

Platoon Score

STDEV

C

11

0.335

0.307

0.028

1.41

1.56

C

11

0.343

0.305

0.038

1.37

1.18

1B

5

0.350

0.308

0.042

1.81

2.02

1B

22

0.340

0.300

0.040

1.17

1.43

2B

17

0.342

0.295

0.046

0.64

0.66

2B

4

0.338

0.304

0.034

0.86

0.86

3B

11

0.343

0.309

0.034

0.95

1.24

3B

5

0.350

0.304

0.046

1.87

0.65

SS

11

0.342

0.312

0.030

0.72

1.51

SS

4

0.338

0.302

0.036

1.02

0.99

OF

34

0.333

0.310

0.023

0.96

1.11

OF

36

0.342

0.303

0.039

1.37

1.72

Utilizing the position to position analysis, it makes sense to isolate for those players that are platoon players relative to their position instead of generalizing based on the population of all platoon players. Players that rank highly based on the mean and variance of their position are rewarded in this analysis. Below is a table sorting the top 5 platoon options relative to their primary position, using the Z-score of their platoon score, based on the position pool of platoon players (“Zplatoonpos”).

Top 5 Left Platoon Options Relative to Positional Pool

Name

Pos

wOBA left

wOBA right

Zl

Zr

Diff

Platoon Score

Zplatoonpos

Brian Dozier

2B

0.376

0.293

1.58

-1.15

2.73

4.3

5.6

Kevin Frandsen

2B

0.376

0.295

1.57

-1.08

2.64

4.1

5.3

Jeff Baker

2B

0.370

0.285

1.40

-1.45

2.85

4.0

5.1

Cody Ross

OF

0.383

0.309

1.80

-0.55

2.34

4.2

2.9

Starling Marte

OF

0.388

0.319

1.96

-0.15

2.12

4.2

2.9

Top 5 Right Platoon Options Relative to Positional Pool

Name

Pos

wOBA right

wOBA left

Zr

Zl

Diff

Platoon Score

Zplatoonpos

Shin-Soo Choo

OF

0.390

0.308

2.61

-0.56

3.16

8.2

4.0

Andre Ethier

OF

0.374

0.292

1.99

-1.04

3.03

6.0

2.7

Adam Lind

1B

0.361

0.286

1.49

-1.24

2.72

4.0

2.0

Ryan Howard

1B

0.361

0.289

1.49

-1.14

2.63

3.9

1.9

John Jaso

C

0.354

0.278

1.20

-1.47

2.67

3.2

1.5

All Platoon Sims

Every single player of the sample is located here. Feel free to play around.

Next Steps

Incorporate salaries to weight platoon score and eliminate those who are cost prohibitive to platooning.

Incorporate total career performance with appropriate weighting into the simulation/compare with three year weighted projections and assess which is more predictive.

Create a team of platoons, and simulate season performance.

Incorporate speed and defense into calculations of platoon score.

Relate the two simulations to provide a more informed simulation of splits.

Comments

Interesting analysis – nice to see some of the usual platoon suspects show up but some unexpected names as well. One thing that the analysis doesn’t appear to account for is the the fact that players with higher over wOBA are less ideal platoon candidates because they can still put up league-average numbers in their weaker matchups. In fact, since the “Platoon Score” actually multiplies by the strong side, you get guys like Chase Utley who are well above average from against both lefties and righties coming up as strong platoon candidates. I think if you factored the weak side into the Platoon Score you would get a better representation of players that aren’t just particularly strong on one side, but are good platoon candidates because they are also below-average on their weak side.

Hey Matt, thanks for the comment. I agree that is one slip in the methodology but it also has to do with the positional pool available at 2B. That position only had a few candidates to begin with so I allowed players slightly above average to slip in. It’s definitely a work in progress and this is the first step towards creating a more comprehensive score. I encourage you to play around with the platoon sims I located in the article. Email me of you have any ideas!

I’m not really familiar with your bootstrapping method, but given the large number of PA versus lefties (or at least the lesser of the two) that it takes to regress a RHB 50% toward the mean, I am skeptical of the large “true” platoon splits that you have for some of the RHB.

For example, Dozier has a 1.28 platoon ratio and Derek Norris has a 1.30 ratio, and both have over an 80 point differential. Given that both Dozier and Norris have only faced around 300-400 lefties each in the least 3 years, you should be regressing their observed platoon ratios 80-90% toward the mean. The mean is only around 1.07 (and a 22 point differential) for RHB I think.

In fact, using a method similar to that in The Book, I have Norris’ regressed platoon wOBA ratio at 1.14, and his regressed platoon differential at 33 points. For Norris, I have 1.12 and 31 points.

I played around with those regressions as well and got similar results for both players. You can argue the accuracy of this method for players with minimum PA’s against — which means the cut off would have to be higher for this analysis to match perfectly with those regressions. Basically what I did regressed based on the uncertantity in each of the components of wOBA and the length (PA) of the bootstrap. I warned that I I would be conservative with Norris, Mercer and Doizer. I kept them in the analysis nonetheless. I’m working on incorporating that regression method while regressing to the mean using the measurable uncertantity in wOBA.

Sorry, Max, I have no idea what you just said. As a test, look at all RH batters with extreme splits in any 3 year period, but limited playing time. See how they do in some out of sample year. I’ll bet that the aggregate is around the mean, nowhere near 1.25 or 1.30 (or 80 point difference).

I rushed that response in between breaks, my apologies. Let my clarify. The bootstrap is the idea of resampling with replacement a single sample of data with an otherwise incalculable standard deviation. For wOBA it’s difficult to approximate it’s uncertainty given a few seasons of data (I know the book uses a certain approximation, this method is simply another way to do the same). Sure wOBA is made of a bunch of binomials like 1B, 2B, 3B, etc that have easily calculable standard deviations — but wOBA has a complex denominator and is the aggregate of these statistics. There is something to be said about the variability in a player whose wOBA value comes from HR’s versus BB’s, 1B’s and 2B’s. This bootstrap takes into account the variability of each component which is defined by some matrix based on the sample data, in R speak:
PA =(rep(1,301))
AB=c(rep(1,259),rep(0,42))
x1B=c(rep(1,51),rep(0,250))
x2B=c(rep(0,51),rep(1,8),rep(0,242))
x3B=c(rep(0,59),rep(1,1),rep(0,241))
HR=c(rep(0,60),rep(1,8), rep(0,233))
BB=c(rep(0,259),rep(1,31), rep(0,11))
IBB=c(rep(0,287),rep(1,3), rep(0,11))
HBP=c(rep(0,290),rep(1,4), rep(0,7))
SF=c(rep(0,294),rep(1,4), rep(0,3))
p5677wOBArightdata= cbind(PA,AB,HR,x1B,x2B,x3B,SF,BB,IBB,HBP).

From the sample, each season is simulated thousands of times and from each season we calculate the wOBA based on the simulated totals. We are left with a sampling distribution with thousands of seasons of wOBA, from which we can pull the standard deviation. That standard deviation is used to regress against the standard deviation of the other players in the sample by this equation (μwOBA +1/ (1+swOBA / σwOBA) * (wOBA- μwOBA)), where we are regressing the mean of the player’s distribution to the observed mean of the larger group.

This process is completed twice, for both versus right data and versus left data. Like I said, I think this method does not regress players with limited success enough. Also the two simulations are not related, as no right data was used to inform left simulation and vice versa. For that reason, I was more interested in each simulated wOBA’s z-score instead of its relation to the other side’s projection. Once I incorporate a more informed sample by using data from both sides, then I would defer to looking at the ratio of right/left and left/right as you did.

Hopefully this was made clearer, and I hope you have some advice/concerns over this way of doing things (other than what I intend to fix up).

But I want to test your theory and will get back to you shortly on those results.

Thanks Max. I am somewhat familiar with that kind of bootstrapping method, but it is above may pay grade! 😉

You certainly want one side to inform the other. If player A had a .250 wOBA from the right and left sides, and player B had a .400 wOBA from the right side and .250 from the left side, even if both players had the same number of appearances from both sides, player B certainly has a larger estimated true wOBA from the left side than player A.

Wow, this is really fascinating work. It’s rare to see a baseball post that makes me feel as wide a range of emotions as this one did – Jeetah’s inclusion made me laugh, the mention of Chase Utley made me cry, Howard’s made me nod until my head fell off, and most of the OF against RHP — Choo, Harper, and Ellsbury, specifically — surprised me. My question: is there a substantial difference in this analysis among outfielders? Since it’s so much more difficult to find offensive production in center, than in the corner spots, I’d be interested to see them broken down as such.

The easiest way for a team to ‘expand the pool’ of 2B/SS/3B/C who can both play the position in the field AND hit right-handed pitching – is to allow natural lefties to actually play 2B/SS/3B/C in the field. Since 1902 (the ‘merger’ of the AL and NL), there have been zero – that is ZERO – lefty MLB fielders at any of those four positions. And I would suspect the same is true throughout the minors – and because of the influence of the draft, right into high school and below as well.

I know when I was a kid that ‘tradition’ went right down to the first year of Little League – first year lefties play OF (because all first-year Little League plays OF) and then lefties either move to 1B or learn to pitch. Why? Because that’s the way it is. Why is that the way it is? Stop being a troublemaker. So lefties either learn to pitch or bulk up and try to become power-hitters (as 1B becomes less defensively-oriented with older players who can throw better) – or quit baseball.

This is one of those instances where an emphasis on empirical data misses the reality of how the universe of data is distorted to begin with. For those positions, the entire universe of player data consists of comparing right-handed position players who have stayed righty at the plate – vs righty position players who have learned to either switch-hit or bat lefty at the plate. There is not a single data point of a lefty learning to field at the position (assuming that there is a natural advantage to fielding righty at them) and batting ‘naturally’ (and more effectively) v RHP.

If the assumption is that teams are occasionally willing to ‘give up a bit of defense’ merely to get a bit of platooning advantage at the plate v RHP; then why not assure oneself of that batting advantage by having a lefty actually play those positions in the field at even a utility-level?

This is a good observation. The problem is an institutional one. How many resources would it take to change the mindset of all the little leagues across America to start playing lefties at all position? How can we be sure that the marginal value in the expansion of the platoon pool will outweigh the loss of defense at that position? In order to build up the pool, lefty players would probably need to play that position since Day 1 of little league to build enough proficiency where they were only marginally worse than a righty playing the same position. Even then, inherently lefties would be at a disadvantage always. However, it is one way to solve the platoon pool in the perfect world, but it would be impossible to implement such a campaign.

By “methodology” I’m assuming that you mean “method.” Methodology is the study of the theory underlying a particular set of methods, not the application of said methods. I know that it sounds like a nit-picky point, but it’s an important one. It’s a mistake that you see quite often in the literature.

Nope.
“Methodology, n. a system of methods used in a particular area of study or activity.”
That may have originally been the meaning of methodology, but it has since gained a conventional meaning which accords with Max’s usage.

Perhaps the author can comment on this, but I was under the impression that this was intended as a legitimate piece of research. Colloquialisms have no place in reports of formal research, or any technical writing, for that matter. “Methodology” has a very specific epistemological meaning, that is to say that methodology is the process through which we learn about methods, and should be used as such. That being said, I’m not prepared to concede that a few naive individuals misusing a word is sufficient for redefining that word. The author describes himself as a “teenage… analyst.” That, combined with the type of work he is attempting leads me to believe that he may have interest in academic work at some point. If, as an academic, you were to submit a manuscript to a reputable journal with the word “methodology” used as you suggest, that article would be rejected and you would be asked to revise and resubmit. I am able to speak from experience on that last point.

To clarify, searching “methodology” in Merriam-Webster’s dictionary yields two definitions. The first is the colloquial, while the second is the technical (and correct) definition. Feel free to use the colloquial definition in your creative writing class, but not in reporting research results.

dude, what a silly hang-up to have. I loath the day when sabermetrics becomes so stale and academic that we have to argue about whether a given dictionary definition of a term is the ‘technical’ or the ‘colloquial’ definition. Let’s all just write in a non-technical language that everybody can understand, attempting whenever possible to be inclusive and interesting, rather than dry and esoteric.

I too have published “serious” writing in a peer-reviewed journal, and I’ve even used your so-called “improper” definition of methodology. Nobody batted an eye, or commented at all.

In the larger, philosophical theater of this debate: you may not like the fact that the English language changes, but it does. And it has, such that methodology now means exactly what Max used it as. In M-W, there’s no line about the new definition being colloquial or non-technical or somehow less valid. That might piss you off, but that’s the way it is. Straight from the source:
“Full Definition of METHODOLOGY

1
: a body of methods, rules, and postulates employed by a discipline : a particular procedure or set of procedures
2
: the analysis of the principles or procedures of inquiry in a particular field
“

I guess it depends where you publish. If you want to publish in a “serious” methodological journal such as Biometrika, Psychometrika, Econometrica (really creative titles, I know…), any of the journals overseen by the American Statistical Association or The Royal Statistical Society, or any one of a number of other quality publications, you had better know the difference between “methodology” and a “method.” I’m assuming that even a largely applied journal such as JQAS might “ding” you. Research methodologists, such as myself, tend to get hung-up on the difference between research that investigates methods (methodological research) and research that applies methods (most every other empirical study). The current study falls into the latter category.

There’s so much noise in wOBA that it takes a long time to get a good sense of “true” talent levels without regressing the stat highly. I’d imagine you’d have more success looking at K/BB splits, since those will become more predictive of true talent faster. This may be something I’ll look in to when I get the time.